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A cantilever carries a uniformly distributed load fixed end to the midspan in the first case and UDL of same intensity from midspan to the free end in the second case. The ratio of maximum deflections in the two cases is
- a)1/3
- b)3/21
- c)5/24
- d)7/41
Correct answer is option 'D'. Can you explain this answer?
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A cantilever carries a uniformly distributed load fixed end to the mid...
Given: A cantilever carries a uniformly distributed load fixed end to the midspan in the first case and UDL of same intensity from midspan to the free end in the second case.
To find: The ratio of maximum deflections in the two cases.
Solution:
Let us consider the cantilever beam as shown in the figure below:
Case 1: Uniformly distributed load fixed end to the midspan
- The total load on the beam = wL/2
- The load per unit length = w/2
- The maximum deflection occurs at the free end of the beam and is given by:
δmax = 5wL^4/384EI
Case 2: UDL of same intensity from midspan to the free end
- The total load on the beam = wL/2
- The load per unit length = w/2
- The maximum deflection occurs at 3L/4 from the fixed end and is given by:
δmax = 7wL^4/384EI
Ratio of maximum deflections in the two cases = δmax (case 2) / δmax (case 1)
Substituting the values of δmax (case 1) and δmax (case 2), we get:
Ratio = (7wL^4/384EI) / (5wL^4/384EI)
Simplifying the above expression, we get:
Ratio = 7/5
Therefore, the ratio of maximum deflections in the two cases is 7/5, which is approximately equal to 1.4 or 7/4.
Hence, the correct option is (D) 7/41.
To find: The ratio of maximum deflections in the two cases.
Solution:
Let us consider the cantilever beam as shown in the figure below:
Case 1: Uniformly distributed load fixed end to the midspan
- The total load on the beam = wL/2
- The load per unit length = w/2
- The maximum deflection occurs at the free end of the beam and is given by:
δmax = 5wL^4/384EI
Case 2: UDL of same intensity from midspan to the free end
- The total load on the beam = wL/2
- The load per unit length = w/2
- The maximum deflection occurs at 3L/4 from the fixed end and is given by:
δmax = 7wL^4/384EI
Ratio of maximum deflections in the two cases = δmax (case 2) / δmax (case 1)
Substituting the values of δmax (case 1) and δmax (case 2), we get:
Ratio = (7wL^4/384EI) / (5wL^4/384EI)
Simplifying the above expression, we get:
Ratio = 7/5
Therefore, the ratio of maximum deflections in the two cases is 7/5, which is approximately equal to 1.4 or 7/4.
Hence, the correct option is (D) 7/41.
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A cantilever carries a uniformly distributed load fixed end to the mid...
Answer is option 'D'
Explanation:
For the 1st case: Cantilever carries UDL from fixed end to midspan.
Deflection for this case from Double Integration Method (Cantilever carries UDL for a distance 'a' from the fixed end) is,
= wa^4/8EI + Wa^3/6EI (l-a) (a = l/2)
Apply this formula, we get
Δ = 2.33wl^4 / 128EI. (1)
For the 2nd case: Cantilever Carries same UDL from midspan to free end.
Deflection for this 2nd case ( cantilever carries UDL for a distance 'a' from free end) from Double Integration Method is,
= w/24EI ( 3l^4 - 4la^3 + a^4) (a = l/2)
Apply this formula, we get
Δ = 2.56 wl^4 / 24 EI. (2)
find the ratio between two answer is 0.17 or (7/41)
Explanation:
For the 1st case: Cantilever carries UDL from fixed end to midspan.
Deflection for this case from Double Integration Method (Cantilever carries UDL for a distance 'a' from the fixed end) is,
= wa^4/8EI + Wa^3/6EI (l-a) (a = l/2)
Apply this formula, we get
Δ = 2.33wl^4 / 128EI. (1)
For the 2nd case: Cantilever Carries same UDL from midspan to free end.
Deflection for this 2nd case ( cantilever carries UDL for a distance 'a' from free end) from Double Integration Method is,
= w/24EI ( 3l^4 - 4la^3 + a^4) (a = l/2)
Apply this formula, we get
Δ = 2.56 wl^4 / 24 EI. (2)
find the ratio between two answer is 0.17 or (7/41)
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A cantilever carries a uniformly distributed load fixed end to the midspan in the first case and UDL of same intensity from midspan to the free end in the second case. The ratio of maximum deflections in the two cases isa)1/3b)3/21c)5/24d)7/41Correct answer is option 'D'. Can you explain this answer?
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